In designing a conventional lens, it is usually required to satisfy the "Abbe sine condition" so as not to have any aberration in the vicinity of the axis of lenses in order to have the rays projecting-in the lens at a contained angle .theta. from the front focus formed into a beam after passing through the lens being parallel with the axis of lens; the height H of the rays (relative to the axis of the lens) is equal to the equivalent focal length F multiplying the tangent function of the incident angle .theta. of the rays, i.e., H=F.multidot. tan .theta.. When using a conventional lens in a scanning device, the incident beam moves at a constant angular velocity will generate a transmitted beam to scan at a speed varied in a manner of trigonometric function curve, i.e., the transmitted beam is unable to move at a constant speed.
In order to obtain a linearly scanning, the lens has to be designed specially. U.S. Pat. No. 3,973,833 discloses a two-element lens for obtaining such feature; the first element of that lens is a bi-convex element, while the second element is a concave-convex one; each of them has its specific curvature. The curvature tolerance and the distance between elements are controlled accurately so as to introduce certain coma for satisfying the relationship H=F.theta..
According to the same basic function, the lens of the present invention comprises three elements so as to obtain higher linearity. Under the same and maximum linearity tolerance condition, the present invention would provide more tolerance during manufacture and assembling.